Remember that famous scene from Star Trek II – Kirk and Khan are engaged in a classic submarine-style fight in a large gas cloud. Spock has analyzed Khan’s tactics and deduced that while Khan is genetically engineered to be brilliant, he is inexperienced. “He’s thinking two-dimensionally,” concludes Spock. Next we see the Enterprise rise up out of the depths of the cloud (relatively speaking) and get a sneak attack on Khan’s ship from behind.

While very dramatic, I always wondered how realistic that scene was. Is there a naive tendency to think two-dimensionally, even when flying out in space? Well, new evidence suggests that perhaps there is.

Neuroscientists have published a study in rats in which they look at the activation of two specialized types of neurons, grid cells and place cells, in rat brains as they navigate a three-dimensional space.

For background, place cells are special neurons that fire in relation to an object’s location. Grid cells fire in relation to an object’s distance. With direction and distance our brains can map where stuff is in relation to us and other stuff. The research, however, has focused on two-dimensional location. Hayman and colleagues therefore decided to study place and grid cells in 3D apparatuses – a climbing wall and a vertical helix.

What they found was that the grid and place cells functioned as predicted in the horizontal plane. However, the grid cells (the ones that encode distance) fired very little or not at all in response to vertical distance. In other words – rat brains are good at mapping how far something is, but not how high it is.

Of course, this is just one study in rats, so we need to explore this issue further, with different mammals (hopefully eventually humans) and in different experimental setups. The experimenters infer that what they found is generalizable to the mammalian brain. This is not unreasonable, but I wonder if primates who were adapted to living in trees developed more of a three-dimensional mental map. If so, did humans retain that enhanced vertical mapping, or did our ancestors lose it on the planes of Africa?

If we assume that the results of this study apply to humans, does that make sense in terms of our own experience. Obviously, we can think three-dimensionally – we can think about how high something is. But we may still retain a horizontal bias. It does seem as if we are more comfortable with the horizontal plane than the vertical dimension. The difference may be between having dedicated hardware that is very good at horizontal reasoning, and having to use more general cortical resources to transpose our spatial reasoning into the vertical dimension. This would give us the ability to map in 3D, but just better and more effortlessly in the horizontal plane.

A horizontal bias has been detected before and published in the psychological literature. Hansen and Essock, for example, found that we process horizontal nature scenes best, then vertical scenes, and least well oblique. This makes sense as these orientations match what we would most encounter in nature. Schipper et al also found a horizontal bias in contour detection. Subjects could still detect contours (in this case ellipses) in the vertical direction, but it took a bit longer, suggesting more processing was required. Durgin et al also found a horizontal bias in our ability to judge distance. There are other studies as well. This phenomenon is referred to as perception anisotropy – a difference in how we perceive the horizontal vs vertical dimension.

It therefore seems that the new study is confirming and explaining the underlying neurological basis for the previously documented horizontal perception bias, and that this bias does extend to humans.

So it does make sense that Khan would have defaulted to the natural human horizontal bias in how we map and think about the world around us. Our brains can deal with the vertical dimension, obviously, but it takes a bit more effort and perhaps training. I imagine that Starfleet has a class that’s titled: “Tactical reasoning in a three-dimensional arena – do not neglect the vertical,” or perhaps, “Attacking on the oblique – how to exploit your opponent’s monkey brains.” Perhaps they even have to adjust for the varying perception biases of different species. Maybe Romulans are better at reasoning in the vertical plane, and Klingons have an oblique bias.

Probably, though, any species that evolved mainly on the surface of a planet would have a similar horizontal bias. That’s where most of the interesting stuff is happening.

25 Responses to “How Mammalian Brains Map in 3D”

“I wonder if primates who were adapted to living in trees developed more of a three-dimensional mental map. If so did humans retain that enhanced vertical mapping, or did our ancestors lose it on the planes of Africa?”

Last week, I was talking with my girlfriend about estimating distances. I made the comment that, in my experience, women are worse than men at judging distances – so we tested it (small data-set, I know). From our chairs, we wrote down the distance and heights of a few things. Interestingly, our horizontal distances were pretty much the same but I was MUCH better at estimating vertical distance. E.g. I estimated the ceiling at 8.5′; whereas, she said 12′ (actual height was 9′). 12′ was absurd to me because I knew I can not dunk a basketball, but I can easily touch the ceiling.

So I wonder if vertical mapping is a learned brain function. If you habituate someone to a 3D environment using, for example, a flight simulator, this should “create” 3D mapping.

On a side note – in the 6th paragraph, why was the number 0 used in “h0pefully?”

@PhysiPhile: Are you taller than your gf? That may partially explain your increased ability to gauge the height of things, especially when you have access to heuristics like how high you can touch and so on. Also, like you said it’s a very small sample size.

I remember listening to the developer commentary in the game Portal, and they mentioned how the early levels repeatedly train the player to look up and not just around so that you will continue to do so in the later levels.

But bats might not have a pure 3D space representation because their sonar has a fairly short range. It doesn’t work much beyond a certain range because the sound attenuates and the delay times get too large.

Fish do tend to stay at the same depth because changes in pressure affect the volume of their swim bladders.

Heh. I’ve been playing a game in development called Shores of Hazeron. It’s a sci-fi game: Build cities on planets to mine resources, design and captain starships, etcetera.

I’ve had occasions where I get briefly lost on my ship because I forget which deck is which (decks are stacked vertically), and I end up in the engine room when I’m trying to go to the hold or airlock.

The amusing thing is that I’m playing a race of bird men, who probably would have better vertical orientation.

As humans, we have naturally have very limited ability to move to change our vertical elevation, but have much greater ability to move about in the other two dimensions. Even for tree dwellers, the vertical axis is severely limited for primates compared to the other two.

Another interesting aspect to consider is orientation. We evolved in an environment with gravity, and a natural sense of (and need to know) “up” and “down”. When pilots loose that orientation, it’s a bad thing.

Nearly all sci-fi tends to work in 2-3/4 D space as if they were flying in the atmosphere or sailing submarines on Earth. Ships tend to move about mostly in the two planer directions while climbing or diving in elevation rather than freely moving about in three dimensions. All ships tend to be oriented the same relative to each other facing “right side up” though there would be no reason to do so in space. (Ships also tend to be designed to defend themselves in 2-3/4 D space in terms of weapons placement.)

In Wrath of Kahn Enterprise changed “elevation” while maintaining its orientation rather than rotating and heading directly for Reliant head on. Why? Because the film makers were using a submarine model of motion to match the theme of submarine style combat, even though the submarine motion doesn’t make sense in the absence of a large gravity well.

Karl – I agree. In sci-fi, like Star Trek, ships are always oriented in the same vertical plane, when that orientation would tend to be randomized unless specific efforts were made or align orientation.

So when the Enterprise and a Klingon ship come face to face, chances are they would be rotated with respect to each other, and just as likely to be “upside down” rather that both upright with respect to each other.

The battle scene in them movie Serenity always makes me aware of our limited ability to manage 3D space. Serenity had to navigate around moving obstacles from all directions and angles.

Every time I see that scene I am aware that it would be nearly impossible to for a human to actually fly through the battle. There are too many oblique moving obstacles to keep track of and still map a safe route.

However – even that scene starts with all the ships on each side on the same the plane.

There may be some aspects of the Star Trek universe that compel orientation of ships with artificial gravity in the same plane. The artificial gravity doesn’t cancel out accelerations in the horizontal planes. Maybe it can’t? Maybe there is an aspect of space that does provide a preferred orientation and the artificial gravity has to align with it.

In the Star Trek universe, the orientation of artificial gravity may have something to do with the natural alignment of dark energy &/or dark matter (or madeupskion particles) relative to the galactic plane.

But, if so, how can you propel your ship in a direction perpendicular to the natural orientation of artificial gravity, or are you condemned to only visit stars relatively close to the “gravitational plane”?

Maybe a ship’s artificial gravity field (weakly) extends so far beyond the ship that it interferes with the fields of other “nearby” ships unless they are aligned with each other.

This is a big issue with sound localization. Our ability localize sound in the horizontal plane is excellent, we can separate out two sounds that are just 1 degree apart if it is straight ahead. Our ability to localize sounds in the vertical plane, hower, is terrible, 10 degrees at best.

To be fair, this is largely a physical issue. Our ears are aligned in the horizontal axis. That means our primary sound localization cues, timing and intensity, are useless for the vertical plane. We have to use much less precise spectral cues in the vertical axis (those little folds of skin around your ears actually distort sounds in very specific ways depending on horizontal and vertical direction, and we are sensitive to that).

However, not all animals have that problem. Barn owls, for example, hunt almost exclusively by hearing where the sounds made by their prey is coming from, and they have to do this very quickly in three dimensions (since they are flying). They do this by have asymmetric ears. This asymmetry means that timing cues (which ear gets the sound first) still work in the horizontal axis, but loudness cues (which ear is the sound loudest in) work in diagonal axis. By comparing timing and level cues they can very accurately determine where a sound is coming from in three dimensions. And in fact it appears there is a structure in the middle part of their sound processing pathway that actually has a map of three dimensional space, with each cell’s location corresponding to the location in space it is sensitive to.

Karl, orientation might not affect translational motion. If you had a gigantic gyroscope, you could still translate it in any direction, you just couldn’t rotated it about its rotational axis. You would have to move it while maintaining its orientation.

“Maybe a ship’s artificial gravity field (weakly) extends so far beyond the ship that it interferes with the fields of other “nearby” ships unless they are aligned with each other.”

I think most submarine captains would tell you that broadcasting your location like that is NOT a good idea when the enemy has homing weapons. Heck, they could just toss a few dumb bombs in your general direction and your own ship would such them right to you.

Many if not most autistic individuals process sensory information differently than non-autistic individuals. It appears that based on this study, autistic individuals are more adept at processing symmetry in the vertical and oblique planes than non-autistics.

Our binocular vision, on a horizontal plane line, enhances horizontal depth perception. A third eye above the other two would increase our vertical depth perception. But it’s more efficient to just move one of the two horizontal eyes up a little, since we’ve not required as much in the way of vertical differentiation. Ever notice that most people are a bit cock-eyed in that way? If you close one eye, and then the other, the scene will move left to right, but also up and down a little, yes? Um, I hope I’m not the only one that’s a little cock-eyed….but if I am, perhaps I have better vertical depth perception! (just worse aesthetics)
Flies are really good in 3D. Their eyes are huge, bulging, multi-faceted globes. Feeding lots of visual information to their brains, which probably only needs a little more room for the garbage-finding apparatus.

If you are moving multiple crafts through space, having some kind of perpendicular standard would reduce the likelihood of accidental crashes. Especially at warp speeds. I could see why you would want all ships following your command to be in similar planes to your ship.

Maybe our brains are 2D because we essentially live in a 2.01D world. The vast majority of us would have traveled thousands of kilometers across the surface of the earth and yet would at most moved less than 10km above or below sea level. For any person born before 1850 most likely they would have moved only a few kilometers up or down and usually over quite a long time.